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人教A版数学必修5第20页习题13:△ABC的三边分别为a,b,c,边BC、CA、AB上的中线分别记为ma,mb,mc,应用余弦定理证明:m_a=1/2(2(b2+c2)-a2)~(1/2),m_b=1/2(2(a2+c2)-b2)~(1/2),m_c=1/2(2(a2+b2)-c2)~(1/2).证明如图1,在△ADC中,由余弦定理,得
Problem A13: The three sides of △ ABC are a, b, c, respectively. The center lines on BC, CA, AB are denoted as ma, mb, mc, respectively. The cosine theorem is applied to prove that m_a = 1/2 (2 (b2 + c2) -a2) ~ (1/2), m_b = 1/2 (2 (a2 + c2) -b2) ~ (1/2), m_c = 1/2 (a2 + b2) -c2) ~ (1/2). Proof as shown in Figure 1, in △ ADC, by the cosine theorem,